Neural Networks Based on a Learnable Two-Dimensional Separable Transform for Image Classification: Theory and Hardware Implementation on FPGA

Objectives. Development of methods for design compact and efficient neural networks for image recognition tasks, as well as their hardware implementation based on FPGA. Methods. The paper proposes the concept of a learnable two-dimensional separable transformation (LST) for designing feedforward neural networks for image recognition tasks. A feature of the LST is the sequential processing of image rows by a fully connected layer, after which the resulting representation is processed by columns using second fully connected layer. In the proposed architecture of a feedforward neural network, the LST is considered as a feature extractor. The hardware implementation of LST-based neural network is based on the concept of in-place computing (shared memory for storing source and intermediate data), as well as using a single set of computing cores to calculate all layers of the neural network. Results. A family of compact neural network architectures LST-1 is proposed, differing in the image embedding size. Experiments on the classification of MNIST handwritten digits have shown the high efficiency of these models: the LST-1-28 network achieves 98.37 % accuracy with 9.5 K parameters, and the more compact LST-1-8 shows 96.53 % accuracy with 1.1 K parameters. Testing of the LST-1-28 hardware implementation confirms the architecture's resistance to parameter quantization errors. Conclusion. The proposed concept of a learnable two-dimensional separable transformation provides the design of compact and efficient neural network architectures characterized by: a small number of learnable parameters, high recognition accuracy, and the regular structure of the algorithm, which makes it possible to obtain their effective implementations based on FPGAs.